Question

if the roots of the quadratic equation ax²-2(a+b)x+a(a+2b+c)=0 are equal. prove that b²=ac. ​

Answer 1

Answer:

ax2+2×(a+b)+...(a+2b+c)=0....(i)ax2+2bx+c=0....(ii)rootsofequation(i)areamaginaryso,B2−4AC<0onD<0[2(a+b)]2−4×a×(a+2b+c)<04a2+4b2+Bab−4a2−8ab−4ac<04(b2−ac)<0b2<ac→(iii)forequation→(ii)D=B24ac=4b2−4ac=4(b2−ac)[∵b2−9c<0]so,D<0orrootsofequation(ii)willbeimaginary